{ "cells": [ { "cell_type": "markdown", "id": "08b633e0", "metadata": {}, "source": [ "Tutorial: inertia relief of a stick aircraft model, MSC Nastran example HA144A\n", "===\n", "\n", "The forward-swept-wing (FSW) airplane with canard of the MSC Nastran example\n", "HA144A, \"FSW Airplane in Level Flight\" (Rodden and Johnson 1994, pp. 181-205),\n", "is a half model of beams and concentrated masses in trimmed 1 g level flight.\n", "The airplane is free: the aerodynamic loads are balanced by the inertia of the\n", "rigid-body motion, and Nastran reports the displacements relative to the\n", "reference support (SUPORT) at GRID 90, in heave and pitch. This is a static\n", "analysis with inertia relief, and this notebook repeats it with pyfe3d:\n", "\n", "1. the structure is built with `BeamC` elements exactly from the bulk data,\n", " with the rigid bars (RBAR) of the wing masses as a transformation of the\n", " degrees of freedom;\n", "2. the mass properties are checked against the grid point weight generator,\n", " and the stiffness model against the published displacements, using the\n", " nodal loads that are in equilibrium with the published bar forces;\n", "3. the published doublet-lattice box forces are transferred to the beam nodes\n", " with Nastran's beam splines (SPLINE2), implemented here, and, as an\n", " alternative, with the coupling of Gryszka and Castro (2026); the inertia\n", " relief of `pyfe3d.solver.apply_inertia_relief` (Barnett et al. 1995),\n", " verified in `tut-inertia-relief.ipynb`, is compared with the published\n", " results;\n", "4. the aerodynamic loads are computed with the vortex lattice method of\n", " AeroSandbox (Sharpe 2021), trimmed for level flight at the conditions of\n", " subcases 1 and 2 of the example, transferred with the same splines, and\n", " the inertia relief is compared again.\n", "\n", "What is exactly reproducible is asserted to the printed precision of the\n", "listing: the mass properties, the displacements given the bar forces, the\n", "global equilibrium, $\\boldsymbol{\\Phi}^\\top \\boldsymbol{F}_{tot} =\n", "\\boldsymbol{0}$ with zero reactions at the reference support, and, with the\n", "published box forces and the splines of Nastran, all the published bar forces\n", "and displacements. The results with the alternative load transfer and with\n", "the AeroSandbox loads are compared with the level of agreement stated in each\n", "section.\n", "\n", "References:\n", "\n", "- Rodden, W. P., Johnson, E. H., *MSC/NASTRAN Aeroelastic Analysis User's\n", " Guide, Version 68*, The MacNeal-Schwendler Corporation, Los Angeles, 1994.\n", " Splines: Eqs. 2-22 to 2-25 (pp. 33-35) and 2-44 to 2-59 (pp. 38-43),\n", " Section 3.3 (pp. 106-108). Example HA144A: description pp. 181-188, input Listing 7-1 (pp. 189-195),\n", " sorted bulk data Listing 7-2 (pp. 196-197), output Listing 7-3 (pp.\n", " 198-205).\n", "- MSC Software, *MSC Nastran 2020 Quick Reference Guide*, Newport Beach,\n", " 2020. Bulk Data entry SPLINE2, pp. 3137-3138.\n", "- Gryszka, M., Castro, S. G. P., *Angled spar battery-wing system for large\n", " all-electric aircraft*, engrXiv preprint, 2026,\n", " https://engrxiv.org/preprint/view/7893/version/10171\n", "- Barnett, A. R., Widrick, T. W., Ludwiczak, D. R., *Closed-Form Static\n", " Analysis with Inertia Relief and Displacement-Dependent Loads Using a\n", " MSC/NASTRAN DMAP Alter*, NASA TM-106836, 1995,\n", " https://ntrs.nasa.gov/citations/19950013233\n", "- Sharpe, P. D., *AeroSandbox: A Differentiable Framework for Aircraft Design\n", " Optimization*, Master's thesis, Massachusetts Institute of Technology, 2021,\n", " https://dspace.mit.edu/handle/1721.1/140023\n", "\n", "This notebook needs `aerosandbox` (version 4.2.10 was used) for the last\n", "part. The structural parts are also checked by\n", "`tests/test_inertia_relief_ha144a.py`, whose model and data this notebook\n", "imports." ] }, { "cell_type": "markdown", "id": "370a2a9c", "metadata": {}, "source": [ "Units, axes and published data\n", "---\n", "\n", "The example uses the lb-ft-s system: the CONM2 entries are weights in lb,\n", "converted to masses in slug by `PARAM,WTMASS,0.031081` $= 1/g$ (p. 192), with\n", "$g = 32.174$ ft/s$^2$. The basic coordinate system has $x$ aft, $y$ to the\n", "right wing and $z$ up; GRID 97 is the nose at $x = 0$, GRID 90 the\n", "reference point at $x = 15$ ft (Figure 7-1, p. 181, and Listing 7-2).\n", "\n", "The published values used below were read from the page images of the\n", "listing, since a text extraction shifts some rows of the tables against the\n", "grid and element numbers. They are stored in\n", "`tests/test_inertia_relief_ha144a.py`, except those of subcase 1, which only\n", "this notebook uses. The box forces are checked here for consistency: each\n", "force equals the pressure times the box area, 6.25 ft$^2$ (checked while\n", "transcribing), the forces sum to the weight of the half model, 8000 lb, and\n", "their moment about the centre of gravity vanishes (the trim)." ] }, { "cell_type": "code", "execution_count": 1, "id": "6cd8e84b", "metadata": { "execution": { "iopub.execute_input": "2026-10-30T23:31:18.825806Z", "iopub.status.busy": "2026-10-30T23:31:18.825632Z", "iopub.status.idle": "2026-10-30T23:31:19.480776Z", "shell.execute_reply": "2026-10-30T23:31:19.480115Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "subcase 1: sum of box forces 7999.9997 lb, canard 2807.1 lb, moment about the c.g. -7.6e-03 lb ft\n", "subcase 2: sum of box forces 8000.0000 lb, canard 2662.7 lb, moment about the c.g. 1.8e-04 lb ft\n" ] } ], "source": [ "import os\n", "import sys\n", "sys.path.insert(0, os.path.join('..', '..', 'tests'))\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from pyfe3d import DOF\n", "from test_inertia_relief_ha144a import (\n", " WTMASS, G_ACC, GRIDS, CBARS, PBARS, CONM2, RBARS, MO_PUB, IS_PUB,\n", " XCG_PUB, BAR_PUB, DISP_PUB, BOX_FORCES_SC2, box_points, build_model,\n", " weight_generator, bar_forces, loads_from_bar_forces, transfer_loads,\n", " weight_loads, solve_inertia_relief, SPLINE2, CORD2R, spline2_loads,\n", " box_moments, resultant)\n", "\n", "# subcase 1, Mach 0.9, q = 40 psf, the quasi-rigid airplane\n", "# box normal forces, Listing 7-3, pp. 199-200, boxes 1000-1007 and 1100-1131\n", "BOX_FORCES_SC1 = np.array([\n", " 1.196130E+03, 2.175811E+02, 8.883241E+01, 7.096516E+01,\n", " 9.470382E+02, 1.563349E+02, 6.773703E+01, 6.250663E+01,\n", " -3.000173E+02, -1.329865E+01, 8.216619E+00, 5.635094E+00,\n", " -1.869569E+00, -4.253911E-01, 1.135240E+01, 7.515286E+00,\n", " 1.049276E+03, 1.124095E+02, 3.016934E+01, 1.173226E+01,\n", " 7.831523E+02, 2.530540E+02, 7.268033E+01, 2.304776E+01,\n", " 6.081699E+02, 2.663550E+02, 1.161488E+02, 4.008963E+01,\n", " 4.804525E+02, 2.304277E+02, 1.301754E+02, 5.613909E+01,\n", " 3.667927E+02, 1.795658E+02, 1.164818E+02, 6.184264E+01,\n", " 2.404014E+02, 1.152592E+02, 8.074072E+01, 5.120200E+01])\n", "# displacements relative to GRID 90, p. 203: GRID: (T3, R1, R2)\n", "DISP_PUB[1] = {\n", " 97: (-6.176795E-03, 0., -6.320098E-04), 98: (-8.566984E-04, 0., -3.320095E-04),\n", " 99: (-9.633963E-04, 0., 3.960283E-04), 100: (-1.065960E-02, 0., 1.688768E-03),\n", " 110: (-2.420829E-03, 7.440053E-04, 2.557247E-03),\n", " 111: (3.972288E-03, 7.440053E-04, 2.557247E-03),\n", " 112: (-8.813946E-03, 7.440053E-04, 2.557247E-03),\n", " 120: (2.554698E-02, 1.262856E-03, 3.255694E-03),\n", " 121: (3.368622E-02, 1.262856E-03, 3.255694E-03),\n", " 122: (1.740775E-02, 1.262856E-03, 3.255694E-03)}\n", "# bar forces, p. 204; the torques of elements 110 and 120 are printed\n", "# truncated in subcase 1 (\"45978E+04\", \"479167E+03\") and are not used (nan)\n", "BAR_PUB[1] = {\n", " 100: (-1.820093E+04, -2.140187E+04, 6.401870E+02, 0.),\n", " 101: (-9.094947E-13, -1.500000E+04, 1.500000E+03, 0.),\n", " 102: (-1.500000E+04, -1.820094E+04, 6.401870E+02, 0.),\n", " 103: (-2.140187E+04, -4.323508E+04, 2.183321E+03, 0.),\n", " 110: (5.796102E+04, 3.544555E+04, 3.899794E+03, np.nan),\n", " 120: (3.026060E+04, 4.318098E+03, 2.246687E+03, np.nan)}\n", "BOX_FORCES = {1: BOX_FORCES_SC1, 2: BOX_FORCES_SC2}\n", "Q_SC = {1: 40., 2: 1200.} # dynamic pressures, psf, TRIM 1 and 2\n", "MACH = 0.9\n", "W = 8000. # lb, weight of the half model\n", "\n", "canard_pts, wing_pts = box_points()\n", "box_pts = np.vstack((canard_pts, wing_pts))\n", "xcg = 15. + XCG_PUB\n", "for sc, F in BOX_FORCES.items():\n", " Mcg = (F*(xcg - box_pts[:, 0])).sum()\n", " print('subcase %d: sum of box forces %.4f lb, canard %.1f lb, '\n", " 'moment about the c.g. %.1e lb ft' % (sc, F.sum(), F[:8].sum(), Mcg))\n", " assert np.isclose(F.sum(), W, rtol=1e-7)\n", " assert abs(Mcg) < 1e-2" ] }, { "cell_type": "markdown", "id": "c9a8f8be", "metadata": {}, "source": [ "The structural model\n", "---\n", "\n", "The bulk data of Listing 7-2 (pp. 196-197) translate into pyfe3d as follows\n", "(`build_model()` in the test module):\n", "\n", "| Bulk data | Content | pyfe3d |\n", "|---|---|---|\n", "| GRID 90-100 | fuselage, $x$ = 0 to 30 ft | nodes |\n", "| GRID 110, 120 | wing elastic axis at 50% chord, 30 deg forward sweep | nodes |\n", "| GRID 111, 112, 121, 122 | wing masses, 2.5 ft forward and aft of the axis | nodes, dependent through RBAR |\n", "| CBAR 100-103 (PBAR 100) | fuselage, $A$ = 2.0, $I_1$ = 0.173611, $I_2$ = 0.15, $J$ = 0.5 ft$^2$, ft$^4$ | `BeamC` |\n", "| CBAR 110, 120 (PBAR 101) | wing, $A$ = 1.5, $I_1$ = 0.173611, $I_2$ = 2.0, $J$ = 0.462963 | `BeamC` |\n", "| MAT1 1 | $E$ = 1.44e9 psf, $G$ = 5.40e8 psf | `BeamProp.E`, `G` |\n", "| CONM2 | 1500 lb at GRID 97-100, 600 lb (forward) and 400 lb (aft) at 111, 121 and 112, 122 | diagonal mass matrix, translations |\n", "| RBAR 111-122 | rigid bars from GRID 110 and 120, all six components dependent | transformation $\\boldsymbol{T}$ |\n", "| SPC1 1 | symmetry: $v$, $r_x$, $r_z$ of the fuselage grids, and $u$ of GRID 90 | `bfix` |\n", "| SUPORT 90 35 | reference support: $w$ and $r_y$ of GRID 90 | `bref` |\n", "\n", "Choices:\n", "\n", "- *Element orientation.* The CBAR orientation vector $(0, 0, 1)$ makes plane 1\n", " vertical; in `BeamC`, a vector in the element plane $xy$ normal to $z$\n", " makes the element $z$ axis vertical, so that $I_1$ = `Iyy`, $I_2$ = `Izz`.\n", "- *Shear.* The PBAR entries have no shear factors $K_1$, $K_2$, i.e. the bars\n", " are rigid in shear; `BeamC` is a Timoshenko element, so `G12` and `G13` are\n", " set to $10^6 E$, while the torsional stiffness stays `G*J`.\n", "- *Rigid bars.* The dependent degrees of freedom of a rigid bar from $A$ to\n", " $B$, $\\boldsymbol{r} = \\boldsymbol{x}_B - \\boldsymbol{x}_A$, are\n", " $\\boldsymbol{u}_B = \\boldsymbol{u}_A + \\boldsymbol{\\theta}_A \\times\n", " \\boldsymbol{r}$ and $\\boldsymbol{\\theta}_B = \\boldsymbol{\\theta}_A$, i.e.\n", " $\\boldsymbol{u} = \\boldsymbol{T} \\boldsymbol{u}_{ind}$ over all degrees of\n", " freedom. The reduced matrices $\\boldsymbol{T}^\\top \\boldsymbol{K}_{C0}\n", " \\boldsymbol{T}$ and $\\boldsymbol{T}^\\top \\boldsymbol{M} \\boldsymbol{T}$ and\n", " loads $\\boldsymbol{T}^\\top \\boldsymbol{F}$ are those of the RBAR, exactly:\n", " the masses at the offset grids give the coupled translational and\n", " rotational inertia at GRID 110 and 120, and a load at an offset grid acts on\n", " the elastic axis with its moment. Stiff beams instead of the rigid bars\n", " would only approximate this, with an ill-conditioned stiffness matrix.\n", " Displacements at the dependent grids are recovered with $\\boldsymbol{T}$.\n", "- *Constraints.* Fuselage and wing lie in the plane $z = 0$; the symmetry\n", " constraints leave two rigid-body modes, heave and pitch, which the\n", " reference support at GRID 90 removes. The beams have no mass (no density\n", " on MAT1, no NSM on PBAR)." ] }, { "cell_type": "code", "execution_count": 2, "id": "fb60fe9d", "metadata": { "execution": { "iopub.execute_input": "2026-10-30T23:31:19.482900Z", "iopub.status.busy": "2026-10-30T23:31:19.482636Z", "iopub.status.idle": "2026-10-30T23:31:19.758319Z", "shell.execute_reply": "2026-10-30T23:31:19.757611Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "degrees of freedom: 66 in total, 42 independent, 16 constrained (SPC1), 2 reference (SUPORT)\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "model = build_model()\n", "idx, ncoords = model['idx'], model['ncoords']\n", "print('degrees of freedom: %d in total, %d independent, %d constrained (SPC1), '\n", " '%d reference (SUPORT)' % (model['N'], model['ind'].sum(),\n", " model['bfix'].sum(), model['bref'].sum()))\n", "\n", "fig, ax = plt.subplots(figsize=(6, 6.5))\n", "for i, p in enumerate(box_pts):\n", " ax.plot(p[1], p[0], '.', color='0.6', ms=4)\n", "# box outlines of the two CAERO1 panels\n", "for (x1, x12, x4, y4, ns, nc) in ((10., 10., 10., 5., 2, 4),\n", " (25., 10., 13.45299, 20., 8, 4)):\n", " for j in range(ns + 1):\n", " eta = j/ns\n", " ax.plot([eta*y4]*2, [x1 + eta*(x4 - x1), x1 + eta*(x4 - x1) + x12],\n", " color='0.8', lw=0.6)\n", " for i in range(nc + 1):\n", " ax.plot([0, y4], [x1 + i/nc*x12, x4 + i/nc*x12], color='0.8', lw=0.6)\n", "for eid, (pid, ga, gb) in CBARS.items():\n", " a, b = ncoords[idx[ga]], ncoords[idx[gb]]\n", " ax.plot([a[1], b[1]], [a[0], b[0]], 'k-', lw=2)\n", "for gb, ga in RBARS.items():\n", " a, b = ncoords[idx[ga]], ncoords[idx[gb]]\n", " ax.plot([a[1], b[1]], [a[0], b[0]], 'b-', lw=1)\n", "for g, w in CONM2.items():\n", " p = ncoords[idx[g]]\n", " ax.plot(p[1], p[0], 'o', ms=4 + w/300, mfc='w', mec='b')\n", "for g in GRIDS:\n", " p = ncoords[idx[g]]\n", " ax.annotate(str(g), (p[1], p[0]), xytext=(4, -10), textcoords='offset points',\n", " fontsize=8)\n", "ax.plot(2.5, xcg, 'r+', ms=12, mew=2, label='centre of gravity')\n", "ax.invert_yaxis()\n", "ax.set_aspect('equal')\n", "ax.set_xlabel('$y$ [ft]')\n", "ax.set_ylabel('$x$ [ft], aft')\n", "ax.set_title('HA144A: beams (black), rigid bars (blue), masses,\\n'\n", " 'aerodynamic boxes (grey) with their quarter-chord points')\n", "ax.legend(loc='lower right')\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "75c5eb59", "metadata": {}, "source": [ "Check 1: mass properties\n", "---\n", "\n", "The grid point weight generator (p. 198) prints the rigid-body mass matrix\n", "about GRID 90, $\\boldsymbol{M}_O = \\boldsymbol{\\Phi}_O^\\top \\boldsymbol{M}\n", "\\boldsymbol{\\Phi}_O$ in weight units, with $\\boldsymbol{\\Phi}_O$ the six\n", "geometric rigid-body modes about GRID 90 (translations and rotations), the\n", "centre of gravity and the inertia about it, I(S). The weights are $4 \\times\n", "1500 + 2 \\times (600 + 400) = 8000$ lb; the centre of gravity, from the\n", "static moments, is at $\\bar{x} = (1500 (0 + 10 + 20 + 30) + 600 (24.61325 +\n", "18.83975) + 400 (29.61325 + 23.83975))/8000 = 17.181625$ ft, i.e. 2.181625 ft\n", "aft of GRID 90, and the pitch inertia about it is $I_{yy} = \\sum_i w_i (x_i -\n", "\\bar{x})^2 = 8.928944 \\times 10^5$ lb ft$^2$. The text of the example rounds\n", "these to 2.182 ft and 892,894 lb ft$^2$ (p. 184)." ] }, { "cell_type": "code", "execution_count": 3, "id": "c21234e3", "metadata": { "execution": { "iopub.execute_input": "2026-10-30T23:31:19.760550Z", "iopub.status.busy": "2026-10-30T23:31:19.760355Z", "iopub.status.idle": "2026-10-30T23:31:19.766195Z", "shell.execute_reply": "2026-10-30T23:31:19.765659Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MO about GRID 90 [lb, lb ft, lb ft^2]:\n", " [[ 8000. 0. 0. 0. 0. -20000. ]\n", " [ 0. 8000. 0. 0. 0. 17453. ]\n", " [ 0. 0. 8000. 20000. -17453. 0. ]\n", " [ 0. 0. 20000. 250000. -145662.5 0. ]\n", " [ 0. 0. -17453. -145662.5 930970.255625 0. ]\n", " [ -20000. 17453. 0. 0. 0. 1180970.255625]]\n", "weight 8000.000000 lb, c.g. 2.181625 ft aft of and 2.500000 ft outboard of GRID 90\n", "I(S) [lb ft^2]:\n", " [[ 200000. 102030. -0. ]\n", " [ 102030. 892894.3545 -0. ]\n", " [ -0. -0. 1092894.3545]]\n", "pitch inertia about the c.g.: 8.928944e+05 lb ft^2 (published 8.928944e+05)\n" ] } ], "source": [ "MO, m, xcg_rel, IS = weight_generator(model)\n", "np.set_printoptions(linewidth=120)\n", "print('MO about GRID 90 [lb, lb ft, lb ft^2]:\\n', np.array2string(MO, precision=6))\n", "print('weight %.6f lb, c.g. %.6f ft aft of and %.6f ft outboard of GRID 90'\n", " % (m, xcg_rel[0], xcg_rel[1]))\n", "print('I(S) [lb ft^2]:\\n', np.array2string(IS, precision=4))\n", "print('pitch inertia about the c.g.: %.6e lb ft^2 (published 8.928944e+05)' % IS[1, 1])\n", "xbar = (1500*(0 + 10 + 20 + 30) + 600*(24.61325 + 18.83975)\n", " + 400*(29.61325 + 23.83975))/8000\n", "assert np.isclose(xbar - 15, XCG_PUB, rtol=1e-12)\n", "assert np.allclose(MO, MO_PUB, rtol=0, atol=1e-6*abs(MO_PUB).max())\n", "assert np.isclose(m, 8000., rtol=1e-14)\n", "assert np.isclose(xcg_rel[0], 2.181625, rtol=1e-12)\n", "assert np.isclose(IS[1, 1], 8.928944e5, rtol=1e-6)\n", "assert np.allclose(IS, IS_PUB, rtol=0, atol=1e-6*abs(IS_PUB).max())" ] }, { "cell_type": "markdown", "id": "0dc03225", "metadata": {}, "source": [ "Check 2: the stiffness model against the published displacements\n", "---\n", "\n", "Fuselage and wing form a tree: given the loads, the bar forces follow from\n", "statics alone. Conversely, the nodal loads that are in equilibrium with the\n", "published bar forces (p. 204) are the assembled element end forces, and\n", "applied to the model they must give the published displacements relative to\n", "GRID 90 (pp. 203-204), if the stiffness, the geometry and the rigid bars are\n", "those of Nastran. These nodal loads contain the aerodynamic loads as Nastran's\n", "splines distribute them and the inertia loads, and are balanced.\n", "\n", "Nastran's CBAR forces are the bending moments of plane 1 at the ends A and\n", "B, $M_{1A}$ and $M_{1B}$, the shear $V_1 = -d M_1/d x$ and the torque $T$.\n", "With the element $z$ axis vertical, they are, from the internal forces\n", "`finte` of `BeamC` (`bar_forces()`): $M_{1A}$ = `finte[4]`, $M_{1B}$ =\n", "`-finte[10]`, $V_1$ = `finte[8]` and $T$ = `finte[9]`. $M_1$ is positive\n", "when the top fibre is in compression: element 101 has $M_{1B} = -1.5 \\times\n", "10^4$ lb ft and the stress $+8.64 \\times 10^4$ psf at the top point C, $y = z =\n", "1$ ft (p. 205).\n", "\n", "Subcases 2 (Mach 0.9, $q$ = 1200 psf) and 3 (Mach 1.3, $q$ = 1151 psf) are\n", "used; subcase 1 is not, since its wing torques are printed truncated." ] }, { "cell_type": "code", "execution_count": 4, "id": "93e37c4c", "metadata": { "execution": { "iopub.execute_input": "2026-10-30T23:31:19.768283Z", "iopub.status.busy": "2026-10-30T23:31:19.768144Z", "iopub.status.idle": "2026-10-30T23:31:19.776728Z", "shell.execute_reply": "2026-10-30T23:31:19.776193Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "subcase 2: rigid-body accelerations [-4.6e-07 -2.1e-07], reactions at GRID 90 [-7.3e-12 1.0e-10]\n", " max |u - u_pub|/max |u_pub| = 1.3e-07, max |bar force - published| = 5.9e-03\n", " GRID w pyfe3d w Nastran r_y pyfe3d r_y Nastran\n", " 97 -6.264163e-03 -6.264164e-03 -6.385623e-04 -6.385624e-04\n", " 98 -8.785403e-04 -8.785404e-04 -3.385621e-04 -3.385622e-04\n", " 99 -1.007080e-03 -1.007080e-03 4.156861e-04 4.156862e-04\n", " 100 -1.125761e-02 -1.125761e-02 1.789539e-03 1.789539e-03\n", " 110 -2.503216e-03 -2.503219e-03 2.716038e-03 2.716038e-03\n", " 111 4.286879e-03 4.286876e-03 2.716038e-03 2.716038e-03\n", " 112 -9.293311e-03 -9.293314e-03 2.716038e-03 2.716038e-03\n", " 120 2.737436e-02 2.737436e-02 3.470037e-03 3.470037e-03\n", " 121 3.604945e-02 3.604945e-02 3.470037e-03 3.470037e-03\n", " 122 1.869926e-02 1.869926e-02 3.470037e-03 3.470037e-03\n", " nodal loads [lb] in equilibrium with the published bar forces:\n", " GRID 97: F_z = -1500.00, net of the weight 0.00\n", " GRID 98: F_z = 728.76, net of the weight 2228.76\n", " GRID 99: F_z = -1555.54, net of the weight -55.54\n", " GRID 100: F_z = -1734.30, net of the weight -234.30\n", " GRID 110: F_z = 1628.47, net of the weight 2628.47\n", " GRID 120: F_z = 2432.61, net of the weight 3432.61\n", "subcase 3: rigid-body accelerations [-1.1e-07 -5.1e-08], reactions at GRID 90 [0.0e+00 4.4e-11]\n", " max |u - u_pub|/max |u_pub| = 4.6e-08, max |bar force - published| = 4.3e-03\n" ] } ], "source": [ "for sc in (2, 3):\n", " f = loads_from_bar_forces(model, BAR_PUB[sc])\n", " out = solve_inertia_relief(model, f)\n", " u = out['ufull']\n", " upub = np.array([DISP_PUB[sc][g] for g in DISP_PUB[sc]])\n", " ufe = np.array([u[DOF*idx[g] + np.array([2, 3, 4])] for g in DISP_PUB[sc]])\n", " err = abs(ufe - upub).max()/abs(upub).max()\n", " bf = bar_forces(model, u)\n", " errf = max(abs(bf[e] - BAR_PUB[sc][e]).max() for e in bf)\n", " print('subcase %d: rigid-body accelerations %s, reactions at GRID 90 %s'\n", " % (sc, np.array2string(out['acc'], precision=1),\n", " np.array2string(out['Rref'], precision=1)))\n", " print(' max |u - u_pub|/max |u_pub| = %.1e, max |bar force - published| = %.1e'\n", " % (err, errf))\n", " if sc == 2:\n", " print(' %5s %14s %14s %14s %14s' % ('GRID', 'w pyfe3d', 'w Nastran',\n", " 'r_y pyfe3d', 'r_y Nastran'))\n", " for g, (w_, rx_, ry_) in DISP_PUB[sc].items():\n", " print(' %5d %14.6e %14.6e %14.6e %14.6e' % (\n", " g, u[DOF*idx[g] + 2], w_, u[DOF*idx[g] + 4], ry_))\n", " print(' nodal loads [lb] in equilibrium with the published bar forces:')\n", " for g in (97, 98, 99, 100, 110, 120):\n", " print(' GRID %d: F_z = %9.2f, net of the weight %9.2f' % (\n", " g, f[DOF*idx[g] + 2], f[DOF*idx[g] + 2] + {110: 1000., 120: 1000.}.get(g, 1500.)))\n", " assert abs(out['acc']).max() < 1e-6\n", " assert err < 2e-6\n", " assert errf < 2e-6*6.2e4" ] }, { "cell_type": "markdown", "id": "d071481d", "metadata": {}, "source": [ "The model reproduces the published displacements to the 7 printed digits,\n", "and the bar forces back. The nodal loads net of the weights show how\n", "Nastran's splines (SPLINE2, p. 182) distribute the aerodynamic loads in\n", "subcase 2: the canard, 2662.7 lb, goes to GRID 98 and 99 only, 2228.8 lb and\n", "434.0 lb (the lever rule, see below); the wing, 5337.3 lb, then puts\n", "$-55.5 - 434.0 = -489.5$ lb on GRID 99 and $-234.3$ lb on GRID 100, and the\n", "rest on the wing grids. A different load transfer gives\n", "different bar forces in the fuselage aft of GRID 90 and in the wing, as shown\n", "below.\n", "\n", "Inertia relief with the published aerodynamic loads\n", "---\n", "\n", "The inertia relief is computed with `pyfe3d.solver.apply_inertia_relief`, through\n", "`solve_inertia_relief()` of the test, which applies the transformation of\n", "the rigid bars, see also `tut-inertia-relief.ipynb` and the user guide page\n", "[Inertia relief](inertia_relief.rst): with the reference support `bref` (here $w$ and\n", "$r_y$ of GRID 90), the rigid-body modes $\\boldsymbol{\\Phi}$ follow from the\n", "stiffness matrix (Barnett et al. 1995, Eq. (19)), the rigid-body\n", "accelerations from $\\boldsymbol{\\Phi}^\\top \\boldsymbol{M} \\boldsymbol{\\Phi}\n", "\\ddot{\\boldsymbol{\\alpha}} = \\boldsymbol{\\Phi}^\\top \\boldsymbol{F}_{ext}$\n", "(Eqs. (21)-(22)), and the displacements relative to the reference support\n", "from the loads plus the d'Alembert forces (Eqs. (23)-(24)). The external\n", "loads are the aerodynamic loads and the weights, $-m g$ along $z$ at each\n", "mass; for a trimmed airplane they are balanced and $\\ddot{\\boldsymbol{\\alpha}}\n", "= \\boldsymbol{0}$. Nastran's trim with `URDD3` $= -1$ (1 g) and `URDD5` $= 0$\n", "(p. 183) is the same balance: the inertia forces of the 1 g vertical\n", "acceleration equal the weights.\n", "\n", "**Load transfer: the beam splines of Nastran.** Nastran interpolates the\n", "deflections of the aerodynamic grid points from those of the structural\n", "grids, $\\boldsymbol{u}_k = \\boldsymbol{G}_{kg} \\boldsymbol{u}_g$, and\n", "transfers the aerodynamic loads with the transpose, $\\boldsymbol{F}_g =\n", "\\boldsymbol{G}_{kg}^\\top \\boldsymbol{F}_k$, which does the same virtual work\n", "(Rodden and Johnson 1994, Eqs. 2-22 to 2-25, pp. 33-35). HA144A uses linear\n", "splines, SPLINE2 (Quick Reference Guide, pp. 3137-3138; theory in Rodden and\n", "Johnson 1994, pp. 38-43): a beam along the $y$ axis of a coordinate system,\n", "with bending and torsion and the flexibility ratio DTOR $= EI/GJ$, which\n", "passes through the deflections of the structural grids, and rigid arms along\n", "its $x$ axis, i.e. a rigid chord perpendicular to the elastic axis (p. 42). A\n", "point at the spline coordinates $(x, y)$ deflects by $w = w_b(y) - x\n", "\\psi(y)$ and rotates by $\\varphi_x = w_b'(y)$ and $\\psi(y)$, with $w_b$ and\n", "$\\psi$ the bending deflection and the twist of the spline. `spline2_matrix()`\n", "of the test module builds $\\boldsymbol{G}_{kg}$ from the fundamental\n", "solutions of the infinite beam, the rigid-body terms and the attachment\n", "flexibilities (Eqs. 2-44 to 2-59); its deflection kernel is that of p. 43,\n", "and the kernels of the rotations follow from the same solutions (derived\n", "here, checked by the exact transfer of the resultants below). The bulk data\n", "(Listing 7-1, pp. 192-193; Listing 7-2, cards 50-57, 69-70, 73-76):\n", "\n", "| Spline | Boxes | SET1 grids | Axis | DZ | DTOR | DTHX | DTHY |\n", "|---|---|---|---|---|---|---|---|\n", "| SPLINE2 1501, canard | 1000-1007 | 98, 99 | CORD2R 1: hinge line, $x$ = 12.5 ft, along $y$ | 0 | 1 | 1 | -1 |\n", "| SPLINE2 1601, wing | 1100-1131 | 99, 100, 111, 112, 121, 122 | CORD2R 2: elastic axis from GRID 100, 30 deg forward sweep | 0 | 1 | -1 | -1 |\n", "\n", "DZ $= 0$ makes the spline pass through the deflections of the grids; a\n", "negative DTHX or DTHY disconnects the slope or the twist (Remark 3, p.\n", "3138), so the wing spline uses the deflections $w$ of its six grids only, and\n", "the canard spline the deflections of GRID 98 and 99 and, through a flexible\n", "attachment, their roll (pp. 182-183).\n", "\n", "**Moments.** The aerodynamic grid point of a doublet-lattice box is its\n", "centre (p. 20), and Nastran applies there the normal force and the moment of\n", "the force, which acts at the quarter chord, about the midchord (p. 186). The\n", "box forces are moved to the box centres with their moments,\n", "$(\\boldsymbol{x}_j - \\boldsymbol{x}_{0j}) \\times \\boldsymbol{F}_j$\n", "(`box_moments()`), and the spline carries both to the structure through its\n", "rigid arms. Since the spline reproduces the rigid-body motions of the grids\n", "exactly (the terms $a_0 + a_1 y - a_2 x$), the transfer conserves the\n", "resultant normal force and its moments about the in-plane axes, by virtual\n", "work (derived here, checked below). The in-plane forces are not transferred,\n", "as in Nastran, whose splines interpolate the normal deflections (Section 3.3,\n", "p. 106)." ] }, { "cell_type": "code", "execution_count": 5, "id": "b263e27f", "metadata": { "execution": { "iopub.execute_input": "2026-10-30T23:31:19.778793Z", "iopub.status.busy": "2026-10-30T23:31:19.778621Z", "iopub.status.idle": "2026-10-30T23:31:19.803076Z", "shell.execute_reply": "2026-10-30T23:31:19.802307Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "subcase 1: |resultant transferred - resultant of the box forces| = 4.5e-11, accelerations [-1.8e-06 -2.7e-07]\n", " max |bar force - published| = 7.6e-03, max |u - u_pub|/max |u_pub| = 1.1e-07\n", " element 103: M1A -2.140187e+04 M1B -4.323508e+04 V1 2.183321e+03 | published -2.140187e+04 -4.323508e+04 2.183321e+03\n", " w of GRID 120 (tip of the elastic axis) 2.554698e-02 | published 2.554698e-02\n", " forces at the quarter chord instead: element 103 M1B -8.78e-04, V1 -1.74e-03, w of GRID 120 -2.89e-04 (relative to Nastran)\n", "subcase 2: |resultant transferred - resultant of the box forces| = 8.0e-11, accelerations [1.6e-07 6.5e-09]\n", " max |bar force - published| = 6.4e-03, max |u - u_pub|/max |u_pub| = 1.2e-07\n", " element 103: M1A -2.271239e+04 M1B -4.598023e+04 V1 2.326783e+03 | published -2.271239e+04 -4.598023e+04 2.326784e+03\n", " w of GRID 120 (tip of the elastic axis) 2.737436e-02 | published 2.737436e-02\n", " forces at the quarter chord instead: element 103 M1B -3.97e-05, V1 -7.85e-05, w of GRID 120 -1.93e-05 (relative to Nastran)\n" ] } ], "source": [ "fw = weight_loads(model)\n", "c_ref = 10. # ft, reference chord\n", "xcg_pt = np.array([xcg, 0., 0.])\n", "qc_pts = box_pts # quarter-chord points\n", "cen_pts = np.vstack(box_points(0.5)) # box centres, aerodynamic grid points\n", "\n", "\n", "def aero_loads_spline(Fz, pts=qc_pts):\n", " r'''Normal forces at the points pts, moved to the box centres with their\n", " moments and transferred with SPLINE2 1501 and 1601'''\n", " return spline2_loads(model, cen_pts, Fz, box_moments(pts, cen_pts, Fz))\n", "\n", "\n", "def resultant_aero(Fz, pts):\n", " F3 = np.zeros((len(Fz), 3))\n", " F3[:, 2] = Fz\n", " return np.concatenate((F3.sum(axis=0), np.cross(pts - xcg_pt, F3).sum(axis=0)))\n", "\n", "\n", "resA = {}\n", "for sc in (1, 2):\n", " F = BOX_FORCES[sc]\n", " fa = aero_loads_spline(F)\n", " # resultant force and moment about the c.g. conserved by the transfer\n", " dres = abs(resultant(model, fa, xcg_pt) - resultant_aero(F, qc_pts)).max()\n", " out = solve_inertia_relief(model, fa + fw)\n", " u, bf = out['ufull'], bar_forces(model, out['ufull'])\n", " errf = max(np.nanmax(abs(bf[e] - BAR_PUB[sc][e])) for e in bf)\n", " upub = np.array([DISP_PUB[sc][g] for g in DISP_PUB[sc]])\n", " ufe = np.array([u[DOF*idx[g] + np.array([2, 3, 4])] for g in DISP_PUB[sc]])\n", " erru = abs(ufe - upub).max()/abs(upub).max()\n", " print('subcase %d: |resultant transferred - resultant of the box forces| = %.1e, '\n", " 'accelerations %s' % (sc, dres, np.array2string(out['acc'], precision=1)))\n", " print(' max |bar force - published| = %.1e, max |u - u_pub|/max |u_pub| = %.1e'\n", " % (errf, erru))\n", " print(' element 103: M1A %.6e M1B %.6e V1 %.6e | published %.6e %.6e %.6e'\n", " % (tuple(bf[103][:3]) + tuple(BAR_PUB[sc][103][:3])))\n", " print(' w of GRID 120 (tip of the elastic axis) %.6e | published %.6e'\n", " % (u[DOF*idx[120] + 2], DISP_PUB[sc][120][0]))\n", " # the canard spline is the lever rule between GRID 98 and 99\n", " w99 = (canard_pts[:, 0] - 10.)/10.\n", " assert np.isclose(fa[DOF*idx[98] + 2], ((1 - w99)*F[:8]).sum(), rtol=1e-12)\n", " Fc = np.r_[F[:8], np.zeros(32)]\n", " assert np.isclose(aero_loads_spline(Fc)[DOF*idx[99] + 2], (w99*F[:8]).sum(),\n", " rtol=1e-12)\n", " assert dres < 1e-10*W*c_ref\n", " assert abs(out['acc']).max() < 1e-5*G_ACC\n", " assert abs(out['Rref']).max() < 1e-9*W\n", " # all published bar forces and displacements, to the printed digits\n", " assert errf < 2e-6*6.2e4\n", " assert erru < 2e-6\n", " resA[sc] = out\n", " # forces applied at the quarter chord, without the moments about the box centres\n", " oq = solve_inertia_relief(model, spline2_loads(model, qc_pts, F) + fw)\n", " bq = bar_forces(model, oq['ufull'])\n", " print(' forces at the quarter chord instead: element 103 M1B %+.2e, V1 %+.2e, '\n", " 'w of GRID 120 %+.2e (relative to Nastran)'\n", " % (bq[103][1]/BAR_PUB[sc][103][1] - 1, bq[103][2]/BAR_PUB[sc][103][2] - 1,\n", " oq['ufull'][DOF*idx[120] + 2]/DISP_PUB[sc][120][0] - 1))" ] }, { "cell_type": "markdown", "id": "5df68a06", "metadata": {}, "source": [ "With the splines of the deck, the published box forces reproduce all the\n", "published bar forces and displacements to the printed digits, in both\n", "subcases: the remaining differences, below $2 \\times 10^{-6}$ of the\n", "largest values, are those of the 7 printed digits of the box forces. The\n", "transferred loads have the resultant force and moment of the box forces to\n", "round-off, the airplane is in trim (accelerations at the level of the\n", "rounding), and the reactions at GRID 90 vanish. The canard spline reduces to\n", "the lever rule between GRID 98 and 99, $F_{99} = \\sum_j F_j (x_j - 10)/10$\n", "and $F_{98} = \\sum_j F_j - F_{99}$, as both grids lie on the canard root at\n", "the same spline coordinate $y = 0$ and the roll goes to the symmetry\n", "constraints.\n", "\n", "Two details matter at this precision. First, the forces must be applied as\n", "Nastran does, at the box centres with their moments: applying them at the\n", "quarter chord through the spline conserves the resultant as well, but the\n", "rigid arms, perpendicular to the swept elastic axis, are not along the flow,\n", "and element 103 changes by up to $2 \\times 10^{-3}$. Second, the ratio\n", "DTOR changes the transfer when the grids lie off the spline axis: with DTOR\n", "$= 0.5$ or $2$ instead of $1$, the shear of element 103 in subcase 2 changes\n", "by about $\\pm 5$%, although the guide states that DTOR has no effect with\n", "zero attachment flexibility (p. 108).\n", "\n", "The alternative: the transfer of Gryszka and Castro (2026)\n", "---\n", "\n", "Section 2.3.5 (p. 8) of Gryszka and Castro (2026) transfers the forces of the\n", "aerodynamic mesh to the structural nodes with the inverse-distance weights of\n", "their Eq. (5),\n", "\n", "$$\n", "w_{ij} = \\frac{1/d_{ij}^2}{\\sum_{k=1}^{n_{points}} 1/d_{kj}^2}\n", "$$\n", "\n", "over the $n_{points}$ nearest nodes $i$ of each aerodynamic point $j$, found\n", "with `scipy.spatial.cKDTree`, applied to the translational degrees of freedom\n", "only. The weights sum to one, which conserves the resultant force, but not\n", "its moment. In the wingbox model of the paper the nodes surround the\n", "aerodynamic points; in a stick model all nodes lie on the beam axes or on the\n", "rigid bars, and the moment of each force about its nodes is lost. Here the\n", "moment of the offset, $w_{ij} (\\boldsymbol{x}_j - \\boldsymbol{x}_i) \\times\n", "\\boldsymbol{F}_j$, is added to the rotational degrees of freedom of node $i$\n", "(`moments=True` of `transfer_loads()`), which conserves force and moment for\n", "any weights; this term is an addition of this notebook. The forces are\n", "applied at the quarter-chord points, the canard boxes are transferred to GRID\n", "98 and 99 ($n_{points} = 2$), and the wing boxes to GRID 99, 100, 111, 112,\n", "121 and 122 ($n_{points} = 3$), the grids of the splines; the loads at the\n", "offset grids reach the elastic axis through the rigid bars." ] }, { "cell_type": "code", "execution_count": 6, "id": "fd3981d3", "metadata": { "execution": { "iopub.execute_input": "2026-10-30T23:31:19.805168Z", "iopub.status.busy": "2026-10-30T23:31:19.804988Z", "iopub.status.idle": "2026-10-30T23:31:19.824318Z", "shell.execute_reply": "2026-10-30T23:31:19.823780Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "subcase 1, forces only : accelerations w_dd = -7.36e-01 ft/s^2, r_y_dd = -3.37e-01 rad/s^2; element 101 V1 = 1229.69 lb, M1B = -12296.9 lb ft\n", "subcase 1, forces and moments: accelerations w_dd = -1.85e-06 ft/s^2, r_y_dd = -2.74e-07 rad/s^2; element 101 V1 = 1500.00 lb, M1B = -15000.0 lb ft\n", "subcase 2, forces only : accelerations w_dd = -7.81e-01 ft/s^2, r_y_dd = -3.58e-01 rad/s^2; element 101 V1 = 1213.25 lb, M1B = -12132.5 lb ft\n", "subcase 2, forces and moments: accelerations w_dd = +1.63e-07 ft/s^2, r_y_dd = +6.54e-09 rad/s^2; element 101 V1 = 1500.00 lb, M1B = -15000.0 lb ft\n" ] } ], "source": [ "WING_GRIDS = [99, 100, 111, 112, 121, 122]\n", "\n", "\n", "def aero_loads_idw(Fz, pts=qc_pts, moments=True, npw=3):\n", " F3 = np.zeros((len(Fz), 3))\n", " F3[:, 2] = Fz\n", " can = (pts[:, 0] < 21.) & (pts[:, 1] < 5.)\n", " return (transfer_loads(model, pts[can], F3[can], [98, 99], 2, moments)\n", " + transfer_loads(model, pts[~can], F3[~can], WING_GRIDS, npw, moments))\n", "\n", "\n", "resC = {}\n", "for sc in (1, 2):\n", " for moments in (False, True):\n", " fa = aero_loads_idw(BOX_FORCES[sc], moments=moments)\n", " out = solve_inertia_relief(model, fa + fw)\n", " bf = bar_forces(model, out['ufull'])\n", " print('subcase %d, %-18s: accelerations w_dd = %+.2e ft/s^2, '\n", " 'r_y_dd = %+.2e rad/s^2; element 101 V1 = %.2f lb, M1B = %.1f lb ft'\n", " % (sc, 'forces and moments' if moments else 'forces only',\n", " out['acc'][0], out['acc'][1], bf[101][2], bf[101][1]))\n", " # equilibrium and reference support, both variants\n", " assert abs(out['Phi'].T @ out['ftot']).max() < 1e-9*W\n", " assert abs(out['Rref']).max() < 1e-9*W\n", " if moments:\n", " resC[sc] = out\n", " assert abs(resultant(model, fa, xcg_pt)\n", " - resultant_aero(BOX_FORCES[sc], qc_pts)).max() < 1e-9*W*c_ref\n", " assert abs(out['acc']).max() < 1e-5*G_ACC\n", " assert np.allclose(bf[101], [0., -1.5e4, 1.5e3, 0.], rtol=0, atol=1e-6*1.5e4)\n", " else:\n", " assert abs(out['acc'][1]) > 0.1" ] }, { "cell_type": "markdown", "id": "bee016e5", "metadata": {}, "source": [ "With the forces only, the transferred loads have a pitching moment about the\n", "centre of gravity that the aerodynamic loads do not have, and the airplane\n", "accelerates in pitch (about $-0.3$ rad/s$^2$): the inertia forces change\n", "the bar forces, e.g. the shear of element 101 is no longer the weight of\n", "GRID 97. With the moments of the offsets, the accelerations vanish to the\n", "rounding of the published box forces, the reactions at GRID 90 vanish, and\n", "element 101 carries $V_1 = 1500$ lb and $M_{1B} = -1.5 \\times 10^4$ lb ft, as\n", "published. The rest of the structure differs from Nastran by the\n", "distribution of the loads, by 0.1-25% (column C of the comparison below):\n", "the inverse-distance weights put positive loads on GRID 99 and 100, where the\n", "wing spline puts negative ones (Check 2), and a part of the canard load on\n", "GRID 99 with a nodal moment at GRID 98.\n", "\n", "Neither transfer drops the moments of the forces: SPLINE2 carries them\n", "through its rigid arms, Eq. (5) needs the added offset term. Eq. (5) itself\n", "weights the forces only (p. 8, \"this weight needs to be added to three\n", "entries ... corresponding to the first three degrees of freedom\")." ] }, { "cell_type": "markdown", "id": "f6394e55", "metadata": {}, "source": [ "The vortex lattice method of AeroSandbox\n", "---\n", "\n", "Following Gryszka and Castro (2026, Section 2.3.4, pp. 7-8), the aerodynamic\n", "loads are computed with the vortex lattice method of\n", "AeroSandbox, with a Prandtl-Glauert correction applied directly to the forces,\n", "$\\boldsymbol{F} = \\boldsymbol{F}_{inc}/\\sqrt{1 - M^2}$. The output of\n", "`VortexLatticeMethod` per panel is a force, $\\boldsymbol{F} = \\rho\n", "(\\boldsymbol{V} \\times \\boldsymbol{l}) \\Gamma$ at the midpoint of the bound\n", "vortex, `vortex_centers`, at the quarter chord of the panel, and no couple:\n", "`moments_geometry` is only the moment of these forces about `xyz_ref`\n", "(`aerosandbox/aerodynamics/aero_3D/vortex_lattice_method.py`, version\n", "4.2.10, lines 227-229 and 327-336). Its transfer must therefore carry the\n", "moments $\\boldsymbol{r} \\times \\boldsymbol{F}$ of the forces: they are moved\n", "to the box centres with their moments and transferred with SPLINE2 1501 and\n", "1601, exactly as the published box forces, so that the comparison isolates\n", "the aerodynamic model. Only the normal force, along $z$, is transferred, as\n", "in Nastran; the in-plane components, the induced drag, are not. The geometry is that of p. 181 and of the CAERO1 entries:\n", "\n", "- wing: chord 10 ft, half span 20 ft, leading edge from $(25, 0)$ to\n", " $(13.45299, 20)$ ft (30 deg forward sweep), incidence 0.1 deg (in Nastran,\n", " the downwash W2GJ = 0.001745 rad of the wing boxes, p. 182), modelled as\n", " the twist of its sections;\n", "- canard: chord 10 ft, half span 5 ft, leading edge at $x = 10$ ft, no sweep,\n", " all-moving about its quarter chord, $x = 12.5$ ft, by the angle $\\delta$\n", " (ELEV), modelled as the twist of its sections (AeroSandbox twists about the\n", " leading edge, so the leading edge is placed on the circle about the quarter\n", " chord);\n", "- flat plates (the camber line of a symmetric airfoil), coplanar at $z = 0$,\n", " mirrored about $y = 0$; the panels are exactly the boxes of CAERO1: 8 x 4 on\n", " the wing and 2 x 4 on the canard, uniform spacing, with the vortex centres at\n", " the box quarter chords;\n", "- fuselage aerodynamics neglected, as in the example (p. 181).\n", "\n", "The vortex lattice method is linear, as the doublet lattice: the loads of\n", "the right half are $\\boldsymbol{F}(\\alpha, \\delta) = \\boldsymbol{F}_0 +\n", "\\alpha \\boldsymbol{F}_\\alpha + \\delta \\boldsymbol{F}_\\delta$, from three runs.\n", "The velocity of the runs only sets a reference dynamic pressure, by which the\n", "forces are scaled to $q$ of the subcase. The trim of level flight solves\n", "for $\\alpha$ and $\\delta$ such that the lift equals the weight, 8000 lb, and\n", "the pitching moment about the centre of gravity vanishes. A uniform factor on\n", "the forces, as the Prandtl-Glauert correction, changes the trim angles but\n", "not the trimmed loads." ] }, { "cell_type": "code", "execution_count": 7, "id": "b8ae0c83", "metadata": { "execution": { "iopub.execute_input": "2026-10-30T23:31:19.826124Z", "iopub.status.busy": "2026-10-30T23:31:19.825991Z", "iopub.status.idle": "2026-10-30T23:31:20.300693Z", "shell.execute_reply": "2026-10-30T23:31:20.300021Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "max distance vortex centre - box quarter-chord point: 1.2e-05 ft (x, y), 1.4e-02 ft (z, the incidence of 0.1 deg)\n", " C_L VLM C_L VLM*beta C_L Nastran C_m,90 VLM C_m,90 VLM*beta C_m,90 Nastran\n", "0 0.01444 0.00629 0.00842 -0.00975 -0.00425 -0.00601\n", "alpha 8.86343 3.86348 5.07098 -4.62481 -2.01591 -2.87093\n", "delta 0.59639 0.25996 0.24614 0.96478 0.42054 0.57153\n" ] } ], "source": [ "import aerosandbox as asb\n", "\n", "flat = asb.Airfoil('naca0010') # symmetric: flat camber line\n", "\n", "\n", "def make_airplane(delta_deg):\n", " ys = np.linspace(0., 20., 9)\n", " wing = asb.Wing(name='wing', symmetric=True, xsecs=[\n", " asb.WingXSec(xyz_le=[25. + (13.45299 - 25.)*y/20., y, 0.], chord=10.,\n", " twist=0.1, airfoil=flat) for y in ys])\n", " d = np.deg2rad(delta_deg)\n", " canard = asb.Wing(name='canard', symmetric=True, xsecs=[\n", " asb.WingXSec(xyz_le=[12.5 - 2.5*np.cos(d), y, 2.5*np.sin(d)], chord=10.,\n", " twist=delta_deg, airfoil=flat) for y in (0., 2.5, 5.)])\n", " return asb.Airplane(name='HA144A', xyz_ref=[xcg, 0., 0.], wings=[wing, canard])\n", "\n", "\n", "def vlm_forces(alpha_deg, delta_deg):\n", " r\"\"\"Vortex centres and forces of the right half, ordered as the boxes\n", " 1000-1007 and 1100-1131, Prandtl-Glauert corrected, per unit dynamic\n", " pressure\"\"\"\n", " op = asb.OperatingPoint(velocity=100., alpha=alpha_deg)\n", " vlm = asb.VortexLatticeMethod(make_airplane(delta_deg), op,\n", " spanwise_resolution=1, chordwise_resolution=4,\n", " spanwise_spacing_function=np.linspace,\n", " chordwise_spacing_function=np.linspace)\n", " vlm.run()\n", " pts, F = vlm.vortex_centers, vlm.forces_geometry\n", " # match each box quarter-chord point to its vortex centre\n", " order = [np.argmin(((pts[:, :2] - p[:2])**2).sum(axis=1)) for p in box_pts]\n", " return pts[order], F[order]/op.dynamic_pressure()/np.sqrt(1 - MACH**2)\n", "\n", "\n", "p0, F0 = vlm_forces(0., 0.)\n", "pa, Fa = vlm_forces(1., 0.)\n", "pd, Fd = vlm_forces(0., 1.)\n", "print('max distance vortex centre - box quarter-chord point: %.1e ft (x, y), '\n", " '%.1e ft (z, the incidence of 0.1 deg)'\n", " % (abs(p0[:, :2] - box_pts[:, :2]).max(), abs(p0[:, 2]).max()))\n", "assert abs(p0[:, :2] - box_pts[:, :2]).max() < 1e-3\n", "f0, fa_, fd_ = F0[:, 2], (Fa - F0)[:, 2]*180/np.pi, (Fd - F0)[:, 2]*180/np.pi\n", "\n", "S, c = 200., 10.\n", "\n", "\n", "def coeffs(fz):\n", " r\"\"\"Lift coefficient and pitching moment coefficient about GRID 90 (nose\n", " up positive), per unit dynamic pressure\"\"\"\n", " return fz.sum()/S, (fz*(15. - box_pts[:, 0])).sum()/(S*c)\n", "\n", "\n", "# rigid derivatives of the listing, Mach 0.9, p. 198-199 (NACA axes, C_L = -C_Z)\n", "nastran = {'0': (8.420787E-03, -6.008128E-03), 'alpha': (5.070976, -2.870932),\n", " 'delta': (2.461395E-01, 5.715300E-01)}\n", "beta = np.sqrt(1 - MACH**2)\n", "print('%-6s %9s %13s %12s %11s %16s %15s' % ('', 'C_L VLM', 'C_L VLM*beta', 'C_L Nastran',\n", " 'C_m,90 VLM', 'C_m,90 VLM*beta', 'C_m,90 Nastran'))\n", "for key, fz in (('0', f0), ('alpha', fa_), ('delta', fd_)):\n", " CL, Cm = coeffs(fz)\n", " print('%-6s %9.5f %13.5f %12.5f %11.5f %16.5f %15.5f' % (\n", " key, CL, CL*beta, nastran[key][0], Cm, Cm*beta, nastran[key][1]))" ] }, { "cell_type": "markdown", "id": "40cc731d", "metadata": {}, "source": [ "The rigid derivatives (per rad) of the doublet-lattice model are those\n", "printed for the rigid, splined airplane (pp. 198-199). The Prandtl-Glauert\n", "factor $1/\\sqrt{1 - 0.81} = 2.29$ applied to all forces overestimates the\n", "lift-curve slope at Mach 0.9 for this low-aspect-ratio configuration, by about\n", "75% for $C_{L_\\alpha}$ and 140% for the canard of aspect ratio 1, whose\n", "effectiveness hardly changes with Mach number; the incompressible values\n", "(columns \"VLM*beta\") are 24% below and 6% above the doublet lattice. As stated\n", "above, this factor changes the trim angles but not the trimmed loads.\n", "\n", "**Trim.** For each subcase, $q (\\boldsymbol{f}_0 + \\alpha\n", "\\boldsymbol{f}_\\alpha + \\delta \\boldsymbol{f}_\\delta)$ is trimmed such that\n", "$\\sum F_z = W$ and $\\sum F_z (\\bar{x} - x) = 0$. The trim angles of\n", "Nastran's rigid airplane follow from its rigid derivatives, with the moment\n", "about the centre of gravity $C_{m,cg} = C_{m,90} + C_L (\\bar{x} - 15)/c$; the\n", "published elastic trim is ANGLEA and ELEV of the listing (pp. 199, 201)." ] }, { "cell_type": "code", "execution_count": 8, "id": "a0e8dc0b", "metadata": { "execution": { "iopub.execute_input": "2026-10-30T23:31:20.302921Z", "iopub.status.busy": "2026-10-30T23:31:20.302764Z", "iopub.status.idle": "2026-10-30T23:31:20.321779Z", "shell.execute_reply": "2026-10-30T23:31:20.320654Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "subcase 1, q = 40 psf: alpha, delta [deg] VLM 5.447 13.733 | Nastran rigid 9.837 28.147 | Nastran elastic 9.694 28.216\n", " canard load: VLM 3037.9 lb, Nastran 2807.1 lb\n", "subcase 2, q = 1200 psf: alpha, delta [deg] VLM 0.085 0.554 | Nastran rigid 0.231 1.035 | Nastran elastic 0.079 1.107\n", " canard load: VLM 3038.4 lb, Nastran 2662.7 lb\n", "subcase 2, direct run at the trim angles: max deviation 2.0e-03 of the max box force\n" ] } ], "source": [ "def trim(fz0, fza, fzd, q):\n", " # moments of the forces at the vortex centres p0\n", " A = q*np.array([[fza.sum(), fzd.sum()],\n", " [(fza*(xcg - p0[:, 0])).sum(), (fzd*(xcg - p0[:, 0])).sum()]])\n", " b = np.array([W - q*fz0.sum(), -q*(fz0*(xcg - p0[:, 0])).sum()])\n", " return np.linalg.solve(A, b)\n", "\n", "\n", "def trim_nastran_rigid(q):\n", " CLreq = W/(q*S)\n", " A = np.array([[nastran['alpha'][0], nastran['delta'][0]],\n", " [nastran['alpha'][1], nastran['delta'][1]]])\n", " b = np.array([CLreq - nastran['0'][0],\n", " -CLreq*XCG_PUB/c - nastran['0'][1]])\n", " return np.linalg.solve(A, b)\n", "\n", "\n", "elastic = {1: (1.691910E-01, 4.924567E-01), 2: (1.373013E-03, 1.932495E-02)}\n", "FB = {}\n", "for sc, q in Q_SC.items():\n", " al, de = trim(f0, fa_, fd_, q)\n", " FB[sc] = q*(f0 + al*fa_ + de*fd_)\n", " assert np.isclose(FB[sc].sum(), W, rtol=1e-12)\n", " assert abs((FB[sc]*(xcg - p0[:, 0])).sum()) < 1e-9*W*c\n", " alr, der = trim_nastran_rigid(q)\n", " print('subcase %d, q = %4.0f psf: alpha, delta [deg] VLM %7.3f %7.3f | '\n", " 'Nastran rigid %7.3f %7.3f | Nastran elastic %7.3f %7.3f'\n", " % (sc, q, np.rad2deg(al), np.rad2deg(de), np.rad2deg(alr), np.rad2deg(der),\n", " *np.rad2deg(elastic[sc])))\n", " print(' canard load: VLM %.1f lb, Nastran %.1f lb' % (FB[sc][:8].sum(),\n", " BOX_FORCES[sc][:8].sum()))\n", "\n", "# check of the linearity, subcase 2: a direct run at the trim angles\n", "al, de = trim(f0, fa_, fd_, Q_SC[2])\n", "pt, Ft = vlm_forces(np.rad2deg(al), np.rad2deg(de))\n", "dev = abs(Q_SC[2]*Ft[:, 2] - FB[2]).max()/abs(FB[2]).max()\n", "print('subcase 2, direct run at the trim angles: max deviation %.1e of the max box force' % dev)\n", "assert dev < 5e-3" ] }, { "cell_type": "markdown", "id": "8e51916a", "metadata": {}, "source": [ "At low dynamic pressure (subcase 1, quasi-rigid), the published elastic trim\n", "is close to the rigid trim from the derivatives. The trim angles of the\n", "vortex lattice model differ from Nastran's by the factor of the lift slopes,\n", "mainly the Prandtl-Glauert factor. The trimmed load distributions can be\n", "compared directly, strip by strip." ] }, { "cell_type": "code", "execution_count": 9, "id": "83c69cb0", "metadata": { "execution": { "iopub.execute_input": "2026-10-30T23:31:20.323963Z", "iopub.status.busy": "2026-10-30T23:31:20.323767Z", "iopub.status.idle": "2026-10-30T23:31:20.501713Z", "shell.execute_reply": "2026-10-30T23:31:20.501039Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "subcase 1, wing strip loads [lb]:\n", " DLM [-299. 17. 1204. 1132. 1031. 897. 725. 488.]\n", " VLM [-357. -50. 1222. 1117. 994. 857. 698. 482.]\n", "subcase 2, wing strip loads [lb]:\n", " DLM [-317. 3. 1173. 1156. 1074. 948. 775. 526.]\n", " VLM [-357. -50. 1221. 1117. 994. 857. 698. 482.]\n" ] } ], "source": [ "yw = 1.25 + 2.5*np.arange(8)\n", "fig, axes = plt.subplots(1, 2, figsize=(10, 3.8))\n", "for ax, sc in zip(axes, (1, 2)):\n", " strips_dlm = BOX_FORCES[sc][8:].reshape(8, 4).sum(axis=1)/2.5\n", " strips_vlm = FB[sc][8:].reshape(8, 4).sum(axis=1)/2.5\n", " ax.plot(yw, strips_dlm, 'ko-', label='wing, doublet lattice (Nastran)')\n", " ax.plot(yw, strips_vlm, 'bs--', label='wing, vortex lattice (AeroSandbox)')\n", " ax.plot(yw[:2], BOX_FORCES[sc][:8].reshape(2, 4).sum(axis=1)/2.5, 'k^-',\n", " label='canard, doublet lattice')\n", " ax.plot(yw[:2], FB[sc][:8].reshape(2, 4).sum(axis=1)/2.5, 'bv--',\n", " label='canard, vortex lattice')\n", " ax.set_title('subcase %d, $q$ = %.0f psf, trimmed' % (sc, Q_SC[sc]))\n", " ax.set_xlabel('$y$ [ft]')\n", " ax.set_ylabel('lift per unit span [lb/ft]')\n", " ax.grid(True, alpha=0.3)\n", "axes[0].legend(fontsize=8)\n", "plt.tight_layout()\n", "plt.show()\n", "for sc in (1, 2):\n", " print('subcase %d, wing strip loads [lb]:\\n DLM %s\\n VLM %s' % (\n", " sc, np.array2string(BOX_FORCES[sc][8:].reshape(8, 4).sum(axis=1), precision=0),\n", " np.array2string(FB[sc][8:].reshape(8, 4).sum(axis=1), precision=0)))" ] }, { "cell_type": "markdown", "id": "094fb589", "metadata": {}, "source": [ "In subcase 1, the rigid vortex lattice and the doublet lattice agree on the\n", "shape of the span loading, including the negative lift of the wing root in the\n", "downwash of the canard; the vortex lattice puts 8% more load on the canard\n", "(3038 lb against 2807 lb), and correspondingly less on the wing. In\n", "subcase 2, the doublet-lattice loads include the elastic deformation of the\n", "forward-swept wing, which twists the tip nose-up (wash-in) and moves lift\n", "outboard, unloading the canard (2663 lb); the one-way analysis here is rigid\n", "and cannot show this: its trimmed loads are nearly the same in both\n", "subcases.\n", "\n", "Inertia relief with the AeroSandbox loads\n", "---\n", "\n", "The trimmed vortex-lattice forces, at the vortex centres, are moved to the\n", "box centres with their moments and transferred with SPLINE2 1501 and 1601,\n", "as the published ones, and the inertia relief is solved with the support at\n", "GRID 90. The transferred loads have the resultant force and moment of the\n", "vortex-lattice forces to round-off, and they are balanced by the trim: the\n", "accelerations, $\\boldsymbol{\\Phi}^\\top \\boldsymbol{F}_{tot}$ and the\n", "reactions vanish to round-off, and element 101 carries the weight of GRID 97\n", "only." ] }, { "cell_type": "code", "execution_count": 10, "id": "72aef17a", "metadata": { "execution": { "iopub.execute_input": "2026-10-30T23:31:20.503898Z", "iopub.status.busy": "2026-10-30T23:31:20.503699Z", "iopub.status.idle": "2026-10-30T23:31:20.515836Z", "shell.execute_reply": "2026-10-30T23:31:20.515290Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "subcase 1: accelerations [ 4.3e-15 -1.4e-14], |Phi^T F_tot| = 2.7e-12 lb, reactions at GRID 90 [-3.6e-12 7.3e-11]\n", " element 101: M1A = 3.64e-12, M1B = -1.500000e+04 lb ft, V1 = 1.500000e+03 lb\n", " |resultant transferred - resultant of the VLM forces| = 5.4e-11\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "subcase 2: accelerations [ 1.4e-14 -1.4e-14], |Phi^T F_tot| = 4.5e-12 lb, reactions at GRID 90 [0.0e+00 6.5e-11]\n", " element 101: M1A = 1.46e-11, M1B = -1.500000e+04 lb ft, V1 = 1.500000e+03 lb\n", " |resultant transferred - resultant of the VLM forces| = 7.3e-11\n" ] } ], "source": [ "resB = {}\n", "for sc in (1, 2):\n", " # the forces act at the vortex centres p0, moved to the box centres\n", " fa = aero_loads_spline(FB[sc], pts=p0)\n", " dres = abs(resultant(model, fa, xcg_pt) - resultant_aero(FB[sc], p0)).max()\n", " out = solve_inertia_relief(model, fa + fw)\n", " bf = bar_forces(model, out['ufull'])\n", " print('subcase %d: accelerations %s, |Phi^T F_tot| = %.1e lb, reactions at GRID 90 %s'\n", " % (sc, np.array2string(out['acc'], precision=1),\n", " abs(out['Phi'].T @ out['ftot']).max(), np.array2string(out['Rref'], precision=1)))\n", " print(' element 101: M1A = %.2e, M1B = %.6e lb ft, V1 = %.6e lb'\n", " % tuple(bf[101][:3]))\n", " print(' |resultant transferred - resultant of the VLM forces| = %.1e' % dres)\n", " assert dres < 1e-10*W*c_ref\n", " assert abs(out['acc']).max() < 1e-10*G_ACC\n", " assert abs(out['Phi'].T @ out['ftot']).max() < 1e-9*W\n", " assert abs(out['Rref']).max() < 1e-9*W\n", " assert np.allclose(bf[101], [0., -1.5e4, 1.5e3, 0.], rtol=0, atol=1e-9*1.5e4)\n", " resB[sc] = out" ] }, { "cell_type": "markdown", "id": "fef374d4", "metadata": {}, "source": [ "Comparison with the published results\n", "---\n", "\n", "Displacements relative to GRID 90 (p. 203) and bar forces (p. 204), for\n", "the two subcases: Nastran; A, the published doublet-lattice box forces\n", "transferred with SPLINE2 (relative difference to Nastran, asserted below\n", "$10^{-5}$); C, the same forces transferred with Eq. (5) plus the moments of\n", "the offsets; B, the trimmed vortex-lattice loads transferred with SPLINE2.\n", "Measured agreement:\n", "\n", "- A agrees with Nastran to the printed digits, within $10^{-6}$;\n", "- C differs from Nastran only by the load transfer: about 10% at the nose, up\n", " to about 25% for the shear of element 103, the torque of element 110 and\n", " the small deflection of GRID 110;\n", "- B differs from Nastran only by the aerodynamic model: in subcase 1\n", " (quasi-rigid), the vortex and doublet lattices differ by the canard share\n", " above, and B is within about 11% of Nastran; in subcase 2, the rigid vortex\n", " lattice also misses the aeroelastic redistribution, and B is up to about\n", " 16% below Nastran for the wing.\n", "\n", "The values of B and C are shown, not asserted: they measure the aerodynamic\n", "model and the load transfer, not the structural model, which Checks 1 and 2\n", "and A verify." ] }, { "cell_type": "code", "execution_count": 11, "id": "26066610", "metadata": { "execution": { "iopub.execute_input": "2026-10-30T23:31:20.518026Z", "iopub.status.busy": "2026-10-30T23:31:20.517861Z", "iopub.status.idle": "2026-10-30T23:31:20.525395Z", "shell.execute_reply": "2026-10-30T23:31:20.524823Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "subcase 1, q = 40 psf\n", " Nastran A A/N-1 C/N-1 B/N-1\n", " w 97 -6.1768e-03 -6.1768e-03 -1e-07 +10.6% -0.6%\n", " r_y 97 -6.3201e-04 -6.3201e-04 -2e-07 +8.3% -0.5%\n", " w 100 -1.0660e-02 -1.0660e-02 +3e-07 +2.4% -3.6%\n", " r_y 100 1.6888e-03 1.6888e-03 +4e-08 -3.8% -4.7%\n", " w 110 -2.4208e-03 -2.4208e-03 -9e-07 +23.6% +1.1%\n", " w 120 2.5547e-02 2.5547e-02 +1e-07 -9.5% -5.6%\n", " r_x 120 1.2629e-03 1.2629e-03 -2e-07 -13.3% -4.3%\n", " r_y 120 3.2557e-03 3.2557e-03 -1e-07 -7.9% -5.5%\n", " w 121 3.3686e-02 3.3686e-02 -7e-08 -9.1% -5.6%\n", " 103 M1A -2.1402e+04 -2.1402e+04 -1e-07 -0.4% -2.8%\n", " 103 M1B -4.3235e+04 -4.3235e+04 +3e-08 -13.2% -6.8%\n", " 103 V1 2.1833e+03 2.1833e+03 +2e-07 -25.9% -10.7%\n", " 110 M1A 5.7961e+04 5.7961e+04 -3e-08 -5.8% -5.3%\n", " 110 V1 3.8998e+03 3.8998e+03 +9e-08 -18.3% -4.5%\n", " 120 M1A 3.0261e+04 3.0261e+04 -2e-07 -11.7% -4.5%\n", " 120 V1 2.2467e+03 2.2467e+03 -2e-07 +8.0% -4.3%\n", "subcase 2, q = 1200 psf\n", " Nastran A A/N-1 C/N-1 B/N-1\n", " w 97 -6.2642e-03 -6.2642e-03 -8e-08 +10.0% -2.0%\n", " r_y 97 -6.3856e-04 -6.3856e-04 -4e-08 +7.8% -1.5%\n", " w 100 -1.1258e-02 -1.1258e-02 +3e-07 +2.0% -8.7%\n", " r_y 100 1.7895e-03 1.7895e-03 +2e-07 -3.7% -10.1%\n", " w 110 -2.5032e-03 -2.5032e-03 -9e-07 +22.0% -2.2%\n", " w 120 2.7374e-02 2.7374e-02 -2e-07 -8.9% -11.9%\n", " r_x 120 1.3580e-03 1.3580e-03 -2e-07 -12.6% -11.0%\n", " r_y 120 3.4700e-03 3.4700e-03 -1e-07 -7.6% -11.3%\n", " w 121 3.6049e-02 3.6049e-02 -8e-08 -8.6% -11.8%\n", " 103 M1A -2.2712e+04 -2.2712e+04 +9e-08 -0.1% -8.4%\n", " 103 M1B -4.5980e+04 -4.5980e+04 -1e-07 -12.6% -12.3%\n", " 103 V1 2.3268e+03 2.3268e+03 -3e-07 -24.7% -16.2%\n", " 110 M1A 6.1642e+04 6.1642e+04 -9e-08 -5.4% -11.0%\n", " 110 V1 4.0611e+03 4.0611e+03 -9e-08 -17.5% -8.3%\n", " 110 T 1.7504e+04 1.7504e+04 -4e-07 -24.4% -15.2%\n", " 120 M1A 3.2741e+04 3.2741e+04 +3e-08 -11.1% -11.8%\n", " 120 V1 2.4326e+03 2.4326e+03 +2e-08 +7.5% -11.6%\n", " 120 T 8.0559e+03 8.0559e+03 -3e-07 +3.7% -12.7%\n" ] } ], "source": [ "rows = [('w 97', 97, 0), ('r_y 97', 97, 2), ('w 100', 100, 0), ('r_y 100', 100, 2),\n", " ('w 110', 110, 0), ('w 120', 120, 0), ('r_x 120', 120, 1), ('r_y 120', 120, 2),\n", " ('w 121', 121, 0)]\n", "frows = [('103 M1A', 103, 0), ('103 M1B', 103, 1), ('103 V1', 103, 2),\n", " ('110 M1A', 110, 0), ('110 V1', 110, 2), ('110 T', 110, 3),\n", " ('120 M1A', 120, 0), ('120 V1', 120, 2), ('120 T', 120, 3)]\n", "for sc in (1, 2):\n", " print('subcase %d, q = %.0f psf' % (sc, Q_SC[sc]))\n", " print(' %-9s %12s %12s %9s %8s %8s' % ('', 'Nastran', 'A', 'A/N-1', 'C/N-1', 'B/N-1'))\n", " uA, uB, uC = resA[sc]['ufull'], resB[sc]['ufull'], resC[sc]['ufull']\n", " for lab, g, k in rows:\n", " n = DISP_PUB[sc][g][k]\n", " a, b, cc = (u_[DOF*idx[g] + 2 + k] for u_ in (uA, uB, uC))\n", " print(' %-9s %12.4e %12.4e %+8.0e %+7.1f%% %+7.1f%%' % (\n", " lab, n, a, a/n - 1, 100*(cc/n - 1), 100*(b/n - 1)))\n", " assert abs(a/n - 1) < 1e-5\n", " bA, bB, bC = (bar_forces(model, u_) for u_ in (uA, uB, uC))\n", " for lab, e, k in frows:\n", " n = BAR_PUB[sc][e][k]\n", " if np.isnan(n):\n", " continue\n", " a, b, cc = bA[e][k], bB[e][k], bC[e][k]\n", " print(' %-9s %12.4e %12.4e %+8.0e %+7.1f%% %+7.1f%%' % (\n", " lab, n, a, a/n - 1, 100*(cc/n - 1), 100*(b/n - 1)))\n", " assert abs(a/n - 1) < 1e-5" ] }, { "cell_type": "code", "execution_count": 12, "id": "e8bade3e", "metadata": { "execution": { "iopub.execute_input": "2026-10-30T23:31:20.527517Z", "iopub.status.busy": "2026-10-30T23:31:20.527355Z", "iopub.status.idle": "2026-10-30T23:31:20.795285Z", "shell.execute_reply": "2026-10-30T23:31:20.794600Z" } }, "outputs": [ { "data": { 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, 2, figsize=(10, 3.8))\n", "fus = [97, 98, 90, 99, 100]\n", "xf = [GRIDS[g][0] for g in fus]\n", "wingg = [100, 110, 120]\n", "yw_ = [GRIDS[g][1] for g in wingg]\n", "for sc, ls in ((1, '--'), (2, '-')):\n", " pub = [0. if g == 90 else DISP_PUB[sc][g][0] for g in fus]\n", " axes[0].plot(xf, 1e3*np.array(pub), 'k' + ls + 'o', label='Nastran, subcase %d' % sc)\n", " axes[1].plot(yw_, 1e3*np.array([DISP_PUB[sc][g][0] for g in wingg]), 'k' + ls + 'o',\n", " label='Nastran, subcase %d' % sc)\n", " for res, col, lab in ((resA, 'g', 'A'), (resC, 'm', 'C'), (resB, 'b', 'B')):\n", " u = res[sc]['ufull']\n", " axes[0].plot(xf, 1e3*u[[DOF*idx[g] + 2 for g in fus]], col + ls + 's', ms=4,\n", " label='%s, subcase %d' % (lab, sc))\n", " axes[1].plot(yw_, 1e3*u[[DOF*idx[g] + 2 for g in wingg]], col + ls + 's', ms=4,\n", " label='%s, subcase %d' % (lab, sc))\n", "axes[0].set_xlabel('$x$ [ft], fuselage GRID 97, 98, 90, 99, 100')\n", "axes[1].set_xlabel('$y$ [ft], elastic axis GRID 100, 110, 120')\n", "for ax in axes:\n", " ax.set_ylabel('$w$ relative to GRID 90 [10$^{-3}$ ft]')\n", " ax.grid(True, alpha=0.3)\n", "axes[1].legend(fontsize=7, ncol=2)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "c3baa3fd", "metadata": {}, "source": [ "Summary\n", "---\n", "\n", "- The `BeamC` model built from the bulk data of HA144A, with the rigid bars\n", " as a transformation of the degrees of freedom and shear-rigid beams,\n", " reproduces the grid point weight generator (weight 8000 lb, centre of\n", " gravity 2.181625 ft aft of GRID 90, pitch inertia 8.928944e5 lb ft$^2$ about\n", " it, the whole matrix MO) and, loaded by the nodal loads in equilibrium with\n", " the published bar forces, the published displacements relative to GRID 90\n", " to the 7 printed digits (subcases 2 and 3).\n", "- Inertia relief with the reference support at GRID 90 (SUPORT 90 35) and the\n", " function `pyfe3d.solver.apply_inertia_relief` gives, for every trimmed load set,\n", " vanishing rigid-body accelerations, $\\boldsymbol{\\Phi}^\\top\n", " \\boldsymbol{F}_{tot} = \\boldsymbol{0}$, zero reactions, and the forces of\n", " element 101, $M_{1B} = -1.5 \\times 10^4$ lb ft and $V_1 = 1500$ lb.\n", "- The linear splines of the deck, SPLINE2 1501 and 1601, implemented from\n", " their theory (Rodden and Johnson 1994, pp. 33-43) and entry (Quick\n", " Reference Guide, pp. 3137-3138), transfer the published doublet-lattice box\n", " forces, applied as Nastran applies them at the box centres with their\n", " moments about the midchord, such that all published bar forces and\n", " displacements are reproduced to the printed digits (relative differences\n", " below $10^{-6}$), in both subcases. The transfer conserves the resultant\n", " force and moment through the rigid arms of the spline; the forces at the\n", " quarter chord instead change element 103 by up to $2 \\times 10^{-3}$, and\n", " the ratio DTOR changes the transfer, contrary to p. 108 of the guide.\n", "- The inverse-distance load transfer of Gryszka and Castro (2026), Eq. (5),\n", " conserves the force; for a stick model the moments of the offsets must be\n", " added to conserve the pitching moment, otherwise the load set is no longer\n", " trimmed and the airplane accelerates in pitch. With the moments, the\n", " results differ from Nastran's by up to about 25%, through the distribution\n", " of the loads alone.\n", "- The vortex lattice method of AeroSandbox gives forces at the bound-vortex\n", " midpoints and no panel moments; their moments are transported to the box\n", " centres and through the splines, with the resultant conserved to\n", " round-off. The trim angles differ from Nastran's mainly through the\n", " uniform Prandtl-Glauert factor, which does not change the trimmed loads. In\n", " the quasi-rigid subcase 1, the span loadings agree in shape and the\n", " structural results are within about 11% of Nastran's; in subcase 2, the\n", " one-way rigid analysis misses the aeroelastic wash-in of the forward-swept\n", " wing, and the wing deflections and loads are up to about 16% lower than\n", " Nastran's elastic trim." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.13" } }, "nbformat": 4, "nbformat_minor": 5 }